I ran across this research article that describes the possibility of plasma waves as being the source of long delayed echoes. This is a PDF file so you will need a display postscript reader such as Adobe Acrobat to read it.
In this article they actually calculate the delay and it agrees well with observed delay times. They also show how microwave frequency transmissions could have delays generated in this manner, however, I am somewhat skeptical of the latter explanation.
The way that frequencies higher than about 28 Mhz can generate long delayed echoes via plasma waves is via non-linear mixing (heterodyning) in the ionosphere.
The idea goes something like this, an amateur radio operator is working moon bounce on 1296 Mhz. At the same time, another signal the operator is completely unaware of has a frequency of 1303 Mhz. They mix in the ionosphere in a non-linear manner producing a difference frequency of 7 Mhz and this 7 Mhz signal can be propagated via a plasma wave and later mix with a 1303 Mhz signal again and reconstitute the original 1296 Mhz signal.
Signals propagate in plasma waves at approximately 1/100th the speed of light so an around the world propagation of a plasma wave would take around 13 seconds. The actual velocity of plasma waves depends on variable factors though, how dense the ionosphere is, the percentage of atoms that are ionized, etc, so for this figure to vary considerably is not unreasonable.
On the surface this sounds like a good potential explanation. However, here is the problem. Most of these long delayed echoes are recognized audibly by human operators. Any modulation of the mixing signal, in this case the 1303 Mhz signal, would be reflected in the difference signal generated and propagated via plasma wave around the earth, and then when that signal is reconstituted by again mixing with the 1303 Mhz signal, those modulation products would be present in the 1296 Mhz signal.
None of the reports of long delayed echoes that I have run across involve any additional modulation of the original signal. I’m not aware of any good reason an unmodulated carrier would be transmitted continuously at 1303 Mhz, but if this mechanism were responsible for long delayed echoes of frequencies higher than 28 Mhz, at least some of them should have resulted from modulated signals and thus carry the modulation of the mixing signal.
Another aspect that I find troubling is that these long delayed echoes often are offset from the original transmission frequencies by a small amount and this theory does not explain that offset. The resulting signals often are at a slightly lower frequency than the original suggesting a reflecting surface or mechanism moving away from the source of transmission and reception.
One aspect that does suggest that long delayed echoes have something to do with the earth’s ionosphere or magnetic field, or possibly the interaction of the earth’s magnetic field with the solar wind is that some observations suggest a correlation with auroral activity.